Answer:
3
256
sq.units
Step-by-step explanation:
Both parabolas cut each other at (0,0) and (16,16)
Area enclosed by these parabolas
=∫
0
16
4
x
dx−∫
0
16
16
x
2
dx
=[
3
2×4×x
3/2
]
0
16
−[
16×3
x
3
]
0
16
=
3
2×4
4
−
3
4
4
=
3
256
sq. units
Select the correct answer.
What is this equation rewritten in exponential form?
log7 343 = 3
Answer:
b.,............................
Step-by-step explanation:
correct answer.
The equation which is rewritten of [tex]log_{7}[/tex] (343) = 3 will be 7³ = 343 which means the option (B) will be correct.
What is a logarithm?The exponent indicates the power to which a base number is raised to produce a given number called a logarithm.
In another word, a logarithm is a different way to denote any number.
By log property of [tex]log_{a}[/tex] b = x ⇒ [tex]a^{x}[/tex] = b
So [tex]log_{7}[/tex] (343) = 3 ⇒ 7³ = 343 will be the correct answer to the question.
For more about logarithm
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f(x) = 2x2 + 4x - 5
g(x) = 6x3 – 2x2 + 3
Find (f + g)(x).
Answer:
4x-5=4x-5
(f+g) (x)=6x³+3Step-by-step explanation:
How many subsets will the sets have? {sheep that have eight legs }
Answer:
256
Step-by-step explanation:
How to find subsets = 2 raise the power n.
N=number of elements in a set.
=2raise the power 8 which is 256.
Solve for f(-2)
PLEASE HELPPPPP
Answer:
5/9
Step-by-step explanation:
f(x) = 5 * 3^x
Let x = -2
f(-2) = 5 * 3^-2
We know a^-b = 1/a^b
= 5 * 1/3^2
= 5/9
F(-2) means the value of x is -2
Replace x with -2 and solve:
3^-2 = 1/9
5 x 1/9 = 5/9
Answer: D.5/9
If there is a 65% chance you will make a free throw, what percent of the
time you will miss? *
Given:
There is a 65% chance you will make a free throw.
To find:
The percent of the time you will miss.
Solution:
If p is the percent of success and q is the percent of failure, then
[tex]p+q=100\%[/tex]
[tex]q=100\%-p[/tex] ...(i)
It is given that there is a 65% chance you will make a free throw. It means the percent of success is 65%. We need to find the percent of the time you will miss. It means we have to find the percent of failure.
Substituting p=65% in (i), we get
[tex]q=100\%-65\%[/tex]
[tex]q=35\%[/tex]
Therefore, there is a 35% chance you will miss the free throw.
APP
A set of quiz scores has a mean of 78 and a standard
deviation of 9. Using a common grading scale where 60
and above is a passing score, what percentage of the
students passed this test?
Explain your answer in terms of the 68-95-99.7 rule.
Answer:
The answer is "There are [tex]97.5\%[/tex] of the students pass in the test ".
Step-by-step explanation:
Since a normally distributed random variable, the practical rule states:
About 68% of the metrics are in the 1 default deviation
About 95% of metrics correspond to 2 standard deviations from the average.
About 3 standard deviations of the average represent 99.7% of the measurement.
We have the following in this problem:
Average of 78, the average 9 default.
Calculating the percentage of students that passed the test.
[tex]Above 60\\\\60 = 78 - 2\times 9[/tex]
Therefore 60 is under the average for two standard deviations.
Its normality test is symmetric, so 50% of such observations are below mean and 50% below mean.
Everything was cleared of the 50 percent above.
Of the 50% below, 95% (within 2 known mean deviations) succeeded.
therefore
[tex]p=0.5+0.5 \times 0.95=0.975[/tex]
Please I need a step by step explanation ASAP.
Calculate the perimeter and area of the shape below:
Answer:
38.6 cm
Step-by-step explanation:
add all of the sides up to get your perimeter
Need your help answering this
always do the PEMDAS it helped me a lot in school
can someone help me out with this question???
Answer:
a
Step-by-step explanation:
If you have two six sided die each labelled one throgh six. Which set of independent events has a higher probability?
Answer : Four sides (1, 2, 3, 4) are less than 5. The probability is 4 out of 6, or 2/3 or 0.6667.
The solution is, the correct answer is B. comparing all the probabilities, the set of independent events with the highest probability is the event of You land on an odd number or you roll a 6.
What is probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
here, we have,
We will consider all the sets of probabilities, the one with the highest probability is the right answer.
a) You roll an odd number and roll a 5: the probability is calculated thus:
1/6 * 3/6
=0.0833
b) You land on an odd number or you roll a 6: the probability is calculated thus:
3/6 +1/6
= 0.6667
c) You roll a six and roll a 4: the probability is calculated thus:
1/6 * 1/4
= 0.0417
d) You roll a 3 and roll an old number: the probability is calculated thus:
1/6 * 3/6
=0.0833
Now, comparing all the probabilities, the set of independent events with the highest probability is the event of You land on an odd number or you roll a 6.
Therefore the correct answer is B.
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ABCD is
square forces 1,2,3,4 and
2.828427125newtons act at
a point in directions
AB, BC, CD, DA and AC.find the resultant.
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Answer:
0
Step-by-step explanation:
Force AC resolves to 2 N in the AB direction and 2 N in the BC direction. Directions AB and CD are opposite, as are directions BC and DA. So, the sum of forces in the AB direction is ...
AB -CD +part of AC = 1 -3 +2 = 0
The sum of forces in the BC direction is ...
BC -DA +part of AC = 2 -4 +2 = 0
The resultant of these 5 forces is 0. There is no net force in any direction.
WILL MAKE BRAINLIEST
Answer:
x=3
Step-by-step explanation:
The ratios need to be the same
AB CB
---------- = ----------
AD ED
3 x
----- = ---------
3+9 12
3 x
----- = ---------
12 12
X must equal 3
Select the correct answer.
Simplify the following expression. Classify the resulting polynomial.
3x(x − 3) + (2x + 6)(-x − 3)
quadratic monomial
quadratic binomial
quadratic trinomial
linear binomial
Answer:
quadratic trinomial
Step-by-step explanation:
3x(x − 3) + (2x + 6)(-x − 3)
Distribute
3x^2 -9x + (2x + 6)(-x − 3)
FOIL
3x^2 -9x + -2x^2 -6x -6x -18
Combine like terms
x^2-21x-18
This has 3 terms so it is a trinomial
The highest power of x is 2 so it is quadratic
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Answer:
x² -21x -18quadratic trinomialStep-by-step explanation:
Eliminating parentheses, we get ...
= (3x)(x) -(3x)(3) +(2x)(-x -3) +6(-x -3)
= 3x² -9x +(2x)(-x) +(2x)(-3) +(6)(-x) +(6)(-3)
= 3x² -9x -2x² -6x -6x -18
= x²(3 -2) +x(-9-6-6) -18
= x² -21x -18
The highest power is 2, so this is a quadratic.
There are 3 terms, so this is a trinomial.
Determine if the triangles are similar. If they are, state the theorem.
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Answer:
ΔGHF ~ ΔMLF by AA theorem
Step-by-step explanation:
In the picture the exponent says 5/3
Answer:
the answer is B
Step-by-step explanation:
[tex] {{ (- 2)}^{3}}^{5 \div 3} = { ( - 2)}^{5} = - 32[/tex]
write -8 form of 2 on up and complete other steps
y _minus 7 equal 10.find y
Answer:
y=17
Step-by-step explanation:
y-7=10
transpose 7
y=10+7
y=17
For a standard normal distribution, find:
P(z > -1.6)
Express the probability as a decimal rounded to 4 decimal places.
Answer:
P(z > -1.76) = 1 - P(z < -1.76) = 1 - 0.0392 = 0.960
HELP PLZ<3
An international company has 28,300 employees in one country. If this represents 34.1% of the company's employees, how many employees does it have in
total?
Round your answer to the nearest whole number.
Answer:
82991 employees
Step-by-step explanation:
One way to solve this would be to solve for 1% of the company's employees and use that value to solve for 100% (100%=the whole part, or the total). We know that
28300 = 34.1%
If we divide a number by itself, it turns into 1. Dividing both sides by 34.1, we get
829.912 = 1%
Then, we know that anything multiplied by 1 is equal to itself. We want to figure out 100%, or the whole part, so we can multiply both sides by 100 to get
100% = 82991
Assume that in the absence of immigration and emigration, the growth of a country's population P(t) satisfies dP/dt = kP for some constant k > 0.
a. Determine a differential equation governing the growing population P(t) of the country when individuals are allowed to immigrate into the country at a constant rate r > 0.
b. What is the differential equation for the population P(t) of the country when individuals are allowed to emigrate at a constant rate r > 0?
Answer:
[tex](a)\ \frac{dP}{dt} = kP + r[/tex]
[tex](b)\ \frac{dP}{dt} = kP - r[/tex]
Step-by-step explanation:
Given
[tex]\frac{dP}{dt} = kP[/tex]
Solving (a): Differential equation for immigration where [tex]r > 0[/tex]
We have:
[tex]\frac{dP}{dt} = kP[/tex]
Make dP the subject
[tex]dP =kP \cdot dt[/tex]
From the question, we understand that: [tex]r > 0[/tex]. This means that
[tex]dP =kP \cdot dt + r \cdot dt[/tex] --- i.e. the population will increase with time
Divide both sides by dt
[tex]\frac{dP}{dt} = kP + r[/tex]
Solving (b): Differential equation for emigration where [tex]r > 0[/tex]
We have:
[tex]\frac{dP}{dt} = kP[/tex]
Make dP the subject
[tex]dP =kP \cdot dt[/tex]
From the question, we understand that: [tex]r > 0[/tex]. This means that
[tex]dP =kP \cdot dt - r \cdot dt[/tex] --- i.e. the population will decrease with time
Divide both sides by dt
[tex]\frac{dP}{dt} = kP - r[/tex]
Find the exact length of the curve. x=et+e−t, y=5−2t, 0≤t≤2 For a curve given by parametric equations x=f(t) and y=g(t), arc length is given by
The length of a curve C parameterized by a vector function r(t) = x(t) i + y(t) j over an interval a ≤ t ≤ b is
[tex]\displaystyle\int_C\mathrm ds = \int_a^b \sqrt{\left(\frac{\mathrm dx}{\mathrm dt}\right)^2+\left(\frac{\mathrm dy}{\mathrm dt}\right)^2} \,\mathrm dt[/tex]
In this case, we have
x(t) = exp(t ) + exp(-t ) ==> dx/dt = exp(t ) - exp(-t )
y(t) = 5 - 2t ==> dy/dt = -2
and [a, b] = [0, 2]. The length of the curve is then
[tex]\displaystyle\int_0^2 \sqrt{\left(e^t-e^{-t}\right)^2+(-2)^2} \,\mathrm dt = \int_0^2 \sqrt{e^{2t}-2+e^{-2t}+4}\,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^2 \sqrt{e^{2t}+2+e^{-2t}} \,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^2\sqrt{\left(e^t+e^{-t}\right)^2} \,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^2\left(e^t+e^{-t}\right)\,\mathrm dt[/tex]
[tex]=\left(e^t-e^{-t}\right)\bigg|_0^2 = \left(e^2-e^{-2}\right)-\left(e^0-e^{-0}\right) = \boxed{e^2-\frac1{e^2}}[/tex]
The exact length of the curve when the parametric equations are x = f(t) and y = g(t) is given below.
[tex]e^2 -\dfrac{1}{e^2 }[/tex]
What is integration?It is the reverse of differentiation.
The parametric equations are given below.
[tex]\rm x=e^t+e^{-t}, \ \ 0\leq t\leq 2\\\\y=5-2t, \ \ \ \ \ 0\leq t\leq 2[/tex]
Then the arc length of the curve will be given as
[tex]\int _0^2 \sqrt{(\dfrac{dx}{dt})^2+(\dfrac{dy}{dx})^2}[/tex]
Then we have
[tex]\rm \dfrac{dx}{dt} = e^t-e^{-t}\\\\ \dfrac{dy}{dt} = -2[/tex]
Then
[tex]\rightarrow \int _0^2 \sqrt{(\dfrac{dx}{dt})^2+(\dfrac{dy}{dx})^2}\ \ dt\\\\\rightarrow \int _0^2 \sqrt{(e^t-e^{-t})^2 + (-2)^2} \ dt\\\\\rightarrow \int _0^2 \sqrt{(e^t+e^{-t})^2} \ dt\\\\\rightarrow \int _0^2 (e^t+e^{-t}) \ dt\\\\\rightarrow (e^2-e^{-2}) \\\\\rightarrow e^2 - \dfrac{1}{e^2}[/tex]
More about the integration link is given below.
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If you make $11.25/hour, how many hours will you need to work to earn $416.25? Please explain how you figured this out.
Answer:
37 hours.
Step-by-step explanation:
Since you need $416.25 start with that. Then divide by $11.25 to see how many hours you need to work. 416.25 divided by 11.25 is 37.
The height h of water in a cylindrical container with radius r = 5 cm is equal to 10 cm. Peter needs to measure the volume of a stone with a complicated shape and so he puts the stone inside the container with water. The height of the water inside the container rises to 13.2 cm. What is the volume of the stone is cubic cm
Answer:
We first find the volume of water without the stone.
V1 = 10 *(π * 52) = 250 π , where π = 3.14
The volume of water and stone is given by
V2 = 13.2 *(π * 52) = 330 π
The volume of the stone is given by
V2 - v1 = 330 π - 250 π = 80 π
= 251.1 cm3
Find x on this triangle
Answer:
3 sqrt(3) =x
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos theta = adj / hyp
cos 30 = x/6
6 cos 30 = x
6 ( sqrt(3)/2) = x
3 sqrt(3) =x
F(x)=3/4x-5, find the slope
Answer:
slope = 3/4
Step-by-step explanation:
Please helps me out !!!
Answer:
x = 74.2
Step-by-step explanation:
Recall: SOH CAH TOA
Reference angle (θ) = 70°
Angle opposite reference angle = x
Adjacent side = 28
Since we have Adjacent side and opposite side, we would apply the trigonometric ratio, TOA:
Tan θ = Opp/Adj
Substitute
Tan 70 = x/27
27*Tan 70 = x
x = 74.2 (nearest tenth)
Given the exchange rate as K1: HK$1.353, calculate Hong Kong dollar equivalent of K70
Answer:
The Hong Kong dollar equivalent of K70 is HK $ 94.71.
Step-by-step explanation:
Given the exchange rate as K1: HK $ 1,353, to calculate Hong Kong dollar equivalent of K70 the following calculation must be performed:
1,353 x 70 = X
94.71 = X
Therefore, the Hong Kong dollar equivalent of K70 is HK $ 94.71.
find the value of 'x' in the given figure
[tex]\boxed{\large{\bold{\textbf{\textsf{{\color{blue}{Answer}}}}}}:)}[/tex]
(2x-20)°+(x+65)°=180°2x-20+x+65=1803x+45=1803x=180-453x=135x=135/3x=45°Mikita is painting a spherical model of a human cell for a science fair. She uses 452.16 square inches of paint to evenly cover the outside of the cell with one coat of paint. What is the diameter of the cell model? (Use 3.14 for the value of π.)
6 in.
12 in.
24 in.
36 in.
Answer:
12
Step-by-step explanation:
Basically you have to divide 3.14 by 452.16 (the formula for area of circle is pi times r squared) and that will get you 144. The square root of 144 is 12 :)
What is the common difference in this sequence: 3, 11, 19, 27,35?
1
ОА.1/8
O B. 3
O C. 8
O D. 12
Answer:
8
Step-by-step explanation:
To determine the common difference, take the second term and subtract the first term
11-3 = 8
Check with the other terms in the sequence
19-11= 8
27-19 = 8
35-27=8
The common difference is 8
Answer:
C. 8
Step-by-step explanation:
There is a common difference between them and that’s 8.
3 + 8 = 11
11 + 8 = 19
19 + 8 = 27
27 + 8 = 35
The table shows the relationship between the time and distance a car travels. What is the missing value?
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Answer:
220
Step-by-step explanation:
When the relationship is proportional, there are several ways you can find missing values. One of them is to recognize the distance for 4 hours will be double the distance for 2 hours.
2 hours : 110 miles
4 hours : 2×110 miles = 220 miles
